Instance checking is considered a central service for data retrieval from description logic (DL) ontologies. In this paper, we propose a revised most specific concept (MSC) method for DL SHI}, which converts instance checking into subsumption problems. This revised method can generate small concepts that are specific-enough to answer a given query, and allow reasoning to explore only a subset of the ABox data to achieve efficiency. Experiments show effectiveness of our proposed method in terms of concept size reduction and the improvement in reasoning efficiency.

In this paper we consider the setting of graph-structured data that evolves as a result of operations carried out by users or applications. We study different reasoning problems, which range from ensuring the satisfaction of a given set of integrity constraints after a given sequence of updates, to deciding the (non-)existence of a sequence of actions that would take the data to an (un)desirable state, starting either from a specific data instance or from an incomplete description of it. We consider a simple action language in which actions are finite sequences of insertions and deletions of nodes and labels, and use Description Logics for describing integrity constraints and (partial) states of the data. We then formalize the data management problems mentioned above as a static verification problem and several planning problems. We provide algorithms and tight complexity bounds for the formalized problems, both for an expressive DL and for a variant of DL-Lite.

The action programming language GOLOG has been found useful for the control of autonomous agents such as mobile robots. In scenarios like these, tasks are often open-ended so that the respective control programs are non-terminating. Before deploying such programs on a robot, it is often desirable to verify that they meet certain requirements. For this purpose, Claßen and Lakemeyer recently introduced algorithms for the verification of temporal properties of GOLOG programs. However, given the expressiveness of GOLOG, their verification procedures are not guaranteed to terminate. In this paper, we show how decidability can be obtained by suitably restricting the underlying base logic, the effect axioms for primitive actions, and the use of actions within GOLOG programs. Moreover, we show that dropping any of these restrictions immediately leads to undecidability of the verification problem.

Recently several inconsistency-tolerant semantics have been introduced for querying inconsistent description logic knowledge bases. Most of these semantics rely on the notion of a repair, defined as an inclusion-maximal subset of the facts (ABox) which is consistent with the ontology (TBox). In this paper, we study variants of two popular inconsistency-tolerant semantics obtained by replacing classical repairs by various types of preferred repair. We analyze the complexity of query answering under the resulting semantics, focusing on the lightweight logic DL-Lite_R. Unsurprisingly, query answering is intractable in all cases, but we nonetheless identify one notion of preferred repair, based upon priority levels, whose data complexity is "only" coNP-complete. This leads us to propose an approach combining incomplete tractable methods with calls to a SAT solver. An experimental evaluation of the approach shows good scalability on realistic cases.

We tackle a long-standing open research problem and prove the decidability of query answering under the stable model semantics for guarded existential rules, where rule bodies may contain negated atoms, and provide complexity results. The results extend to guarded Datalog+/- with negation, and thus provide a natural and decidable stable model semantics to description logics such as ELHI and DL-LiteR.

In the last few years, there has been a large effort for analyzing the computational properties of reasoning in fuzzy description logics. This has led to a number of papers studying the complexity of these logics, depending on the chosen semantics. Surprisingly, despite being arguably the simplest form of fuzzy semantics, not much is known about the complexity of reasoning in fuzzy description logics w.r.t. witnessed models over the Gödel t-norm. We show that in the logic G-IALC, reasoning cannot be restricted to finitely-valued models in general. Despite this negative result, we also show that all the standard reasoning problems can be solved in exponential time, matching the complexity of reasoning in classical ALC.

We investigate conjunctive query inseparability of description logic (DL) knowledge bases (KBs) with respect to a given signature, a fundamental problem for KB versioning, module extraction, forgetting and knowledge exchange. We study the data and combined complexity of deciding KB query inseparability for fragments of Horn-ALCHI, including the DLs underpinning OWL 2 QL and OWL 2 EL. While all of these DLs are P-complete for data complexity, the combined complexity ranges from P to EXPTIME and 2EXPTIME. We also resolve two major open problems for OWL 2 QL by showing that TBox query inseparability and the membership problem for universal UCQ-solutions in knowledge exchange are both EXPTIME-complete for combined complexity.

Two-way regular path queries (2RPQs) have received increased attention recently due to their ability to relate pairs of objects by flexibly navigating graph structured data. They are present in property paths in SPARQL 1.1, the new standard RDF query language, and in the XML query language XPath. In line with XPath, we consider the extension of 2RPQs with nesting, which allows one to require that objects along a path satisfy complex conditions, in turn expressed through (nested) 2RPQs. We study the computational complexity of answering nested 2RPQs and conjunctions thereof (CN2RPQs) in the presence of domain knowledge expressed in description logics (DLs). We establish tight complexity bounds in data and combined complexity for a variety of DLs, ranging from lightweight DLs (DL-Lite, EL) up to highly expressive ones. Interestingly, we are able to show that adding nesting to (C)2RPQs does not affect worst-case data complexity of query answering for any of the considered DLs. However, in the case of lightweight DLs, adding nesting to 2RPQs leads to a surprising jump in combined complexity, from P-complete to ExpTime-complete.

We study learning of description logic TBoxes in Angluin et al.’s framework of exact learning via queries. We admit entailment queries (“is a given subsumption entailed by the target TBox?”) and equivalence queries (“is a given TBox equivalent to the target TBox?”), assuming that the signature and logic of the target TBox are known. We present three main results: (1) TBoxes formulated in DL-Lite with role inclusions and composite concepts on the right-hand side of concept inclusions can be learned in polynomial time; (2) EL TBoxes with only concept names on the right-hand side of concept inclusions can be learned in polynomial time; and (3) EL TBoxes cannot be learned in polynomial time. It follows that non-polynomial time learnability of EL TBoxes is caused by the interaction between existential restrictions on the right and left-hand sides of concept inclusions. We also show that neither entailment nor equivalence queries alone are sufficient in cases (1) and (2) above.

In Description Logic (DL) knowledge bases (KBs) information is typically captured by crisp concepts. For many applications, querying the KB by crisp query concepts is too restrictive. A controlled way of gradually relaxing a query concept can be achieved by the use of concept similarity measures. In this paper we formalize the task of instance query answering for crisp DL KBs using concepts relaxed by concept similarity measures. We investigate computation algorithms for this task in the DL EL, their complexity and properties for the employed similarity measure regarding whether unfoldable or general TBoxes are used.